Expressions A time line is a useful way to represent important dates and events throughout history. It’s common to divide a historical time line into events that occurred either BC (to the left of zero) or AD (to the right of zero). The year you’re living in right now takes place in AD.

When performing mathematical operations involving dates, we can think of a historical time line as a number line. On the number line, the years increase from left to right. If zero represents the origin, the years to the right of zero are considered positive numbers and the years to the left of zero are considered negative numbers. Using this analogy, here are some events that might appear on a historical number line:

Event Historical Time Line Number Line
The first ancient games take place in Olympia, Greece. 776 BC -776
Construction begins on the Great Wall of China. 221 BC -221
World War I begins in central Europe. AD 1914 1,914 (or 1914)
Use these ideas about time lines and number lines to answer the questions that follow.
Part D
Are the expressions you developed in Part A and Part C the same? Why or why not?
Part E
Christopher Columbus set sail from Spain in 1492. In what year did the Civil War end?

Part F
The year the Greek city of Helike disappeared is times the year the US Civil War ended. Let w represent the year the Civil War ended. Write an expression in terms of w to represent the year of Helike’s disappearance.

Part G
Use the results from Part E and Part F to determine the year Helike disappeared. Express your answer in terms of BC or AD.

Part H
Using the results from parts D through G, write an expression that represents the number of years elapsed between the disappearance of the Greek city of Helike and the end of the US Civil War. Write the expression in terms of c and w. Then solve the expression to find out how many years separate these two events.